آمار
| تعداد نشریات | 6 |
| تعداد شماره‌ها | 131 |
| تعداد مقالات | 1,634 |
| تعداد مشاهده مقاله | 1,915,268 |
| تعداد دریافت فایل اصل مقاله | 1,769,840 |
The Wiener Index of the Associate Graph of $Z_n$ | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 فروردین 1405 اصل مقاله (444.74 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30991.2697 | ||
| نویسندگان | ||
| C.M. Barasara* 1؛ K.D. Thakor2 | ||
| 1Department of Mathematics, Hemchandracharya North Gujarat University, Patan - 384265, Gujarat, India | ||
| 2Research Scholar, Department of Mathematics, Hemchandracharya North Gujarat University, Patan - 384265, Gujarat, India | ||
| چکیده | ||
| Let $R$ be a commutative ring, the associate graph, $Ass(R)$ of ring $R$ has the elements of ring $R$ as vertices and two distinct vertices $u$ and $v$ are adjacent if $u$ and $v$ are associate elements of $R$. In this article we investigate the Wiener index of $Ass(\mathbb{Z}_{n})$ and its line graph for all $n\in \mathbb{N}$. We also give some characterization results regarding degree, diameter, girth, clique number, chromatic number, domination number, and independence number of $Ass(\mathbb{Z}_{n})$ and $L\left( Ass(\mathbb{Z}_{n}) \right)$. | ||
| کلیدواژه‌ها | ||
| associate graph؛ Wiener index؛ line graph؛ commutative ring | ||
| مراجع | ||
|
[1] T. Asir and V. Rabikka, The Wiener index of the zero-divisor graph of Zn, Discrete Appl. Math. 319 (2022), no. 38, 461–471. https://doi.org/10.1016/j.dam.2021.02.035
[2] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208–226. https://doi.org/10.1016/0021–8693(88)90202-5
[3] L. Boro, M.M. Singh, and J. Goswami, Line graph associated to the intersection graph of ideals of rings, J. Math. Comput. Sci. 11 (2021), no. 3, 2736–2745. https://doi.org/10.28919/jmcs/5567
[4] L. Boro, M.M. Singh, and J. Goswami, On the line graphs associated to the unit graphs of rings, Palestine J. Math. 11 (2022), no. 4, 139–145.
[5] D.M. Burton, Elementary Number Theory, McGraw-Hill Companies, 2011.
[6] H.J. Chiang-Hsieh, P.F. Lee, and H.J. Wang, The embedding of line graphs associated to the zero-divisor graphs of commutative rings, Israel J. Math. 180 (2010), no. 1, 193–222. https://doi.org/10.1007/s11856-010-0101-2
[7] J. Clark and D.A. Holton, A First Look at Graph Theory, Allied Publishers Ltd., 1995.
[8] M. Dehmer and F. Emmert-Streib, Quantitative Graph Theory: Mathematical Foundations and Applications, CRC Press, 2014.
[9] J. Devillers and A. Balaban, Topological indices and related descriptors in QSAR and QSPR, Gordon and Breach Science Publishers, 1999.
[10] A. Dobrynin, R. Entringer, and I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math. 66 (2001), no. 3, 211–249. https://doi.org/10.1023/A:1010767517079
[11] A. Dobrynin and A. Iranmanesh, Wiener index of edge thorny graphs of catacondensed benzenoids, Mathematics 8 (2020), no. 4, 467–479. https://doi.org/10.3390/math8040467
[12] K. Elahi, A. Ahmad, and R. Hasni, Construction algorithm for zero divisor graphs of finite commutative rings and their vertex-based eccentric topological indices, Mathematics 6 (2018), no. 12, 301–309. https://doi.org/10.3390/math6120301
[13] N. Gohain, T. Ali, and A. Akhtar, Reducing redundancy of codons through total graph, Current Research in Bioinformatics 4 (2015), no. 1, 1–6. https://doi.org/10.3844/ajbsp.2015.1.6
[14] J. Goswami and H.K. Saikia, On the line graph associated to the line graph of a module, Matematika 31 (2015), no. 1, 7–13. https://doi.org/10.11113/matematika.v31.n1.676
[15] I. Gutman and O.E. Polansky, Mathematical Concept in Organic Chemistry, Springer-Verlag, 1986.
[16] F. Harary, Graph Theory, Addison-Wesley Publishing Company, 1969.
[17] F. Harary and R.Z. Norman, Some properties of line digraphs, Rendiconti del Circolo Matematico di Palermo 9 (1960), no. 2, 161–169. https://doi.org/10.1007/BF02854581
[18] T. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1988.
[19] I.N. Herstein, Topics in Algebra, John Wiley & Sons, 1975.
[20] H. Hosaya, Topological index. a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Japan 44 (1971), no. 9, 2332–2339. https://doi.org/10.1246/bcsj.44.2332
[21] N.J. Khalel and N.E. Arif, Associate graph of a commutative ring, J. Discrete Math. Sci. Cryp. 26 (2023), no. 7, 1883–1887. https://doi.org/10.47974/JDMSC-1679
[22] M. Sarmah and K. Patra, Line graph associated to total graph of idealization, Afrika Matematika 27 (2015), no. 3, 485–490. https://doi.org/10.1007/s13370-015-0355-2
[23] M.J. Subhakar, Associate ring graphs, Mapana J. Sciences 9 (2010), no. 1, 31–40. https://doi.org/10.12723/mjs.16.5
[24] C. Susanth and S.J. Kalayathankal, The sum and product of independence numbers of graphs and their line graphs, J. Inf. Math. Sci. 6 (2014), no. 2, 77–85.
[25] H. Wiener, Structural determination of paraffin boiling points, J. American Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005
[26] Z.P. Zoran and S.P. Zoran, The line graph associated to the total graph of commutative rings, Ars Combin. 127 (2016), 185–195. | ||
|
آمار تعداد مشاهده مقاله: 421 تعداد دریافت فایل اصل مقاله: 432 |
||